Write an equation of a parabola that passes through the point (2,4) with vertex (-1,-1) in vertex form.

An applicable equation of a vertical parabola in vertex form is:

y-k = a(x-h)^2

Let x=2, y=4, h=-1 and k=-1, where (h,k) is the vertex.  Then,

4-(-1) = a(2-[-1])^2, which becomes 5 = a(9).  Therefore, a = 5/9, and the 
equation of the parabola is

y+1 = (5/9)(x+1)